Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024358 | Nonlinear Analysis: Real World Applications | 2018 | 17 Pages |
Abstract
In this paper, we concern the 3D nematic liquid crystal equations and prove three almost Serrin-type blow-up criteria for the breakdown of local in time smooth solutions in terms of pressure and gradient of the orientation field. More precisely, let Tâ be the maximal time of the local smooth solution, then Tâ<+â if and only if â«0TââââP(â
,t)âLx1pâLx2qâLx3rβ+ââd(â
,t)âL48dt=â, with 2β+1p+1q+1r=2 and 2â¤p,q,râ¤â,1â(1p+1q+1r)â¥0,and â«0TâââââP(â
,t)âLx1pâLx2qâLx3rβ+ââd(â
,t)âL48dt=â, with 2β+1p+1q+1r=3 and 1â¤p,q,râ¤â,1â(12p+12q+12r)â¥0,and â«0Tââââ3P(â
,t)âLx3γâLx1x2αβ+ââd(â
,t)âL48dt=â, with 2β+1γ+2α=kâ[2,3) and 3kâ¤Î³â¤Î±<1kâ2.
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Authors
Qiao Liu, Pei Wang,